Question: Express this quotient in scientific notation: ${\frac{2.300\times 10^{6}} {5.0\times 10^{3}}}$
Solution: Start by collecting like terms together. $= {\frac{2.300} {5.0}} \times{\frac{10^{6}} {10^{3}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.46 \times 10^{6\,-\,3}$ $= 0.46 \times 10^{3}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.46$ is the same as $4.60 \div 10$ , or $4.60 \times 10^{-1}$ $ = {4.60 \times 10^{-1}} \times 10^{3} $ $= 4.60\times 10^{2}$